Distorted Noise: Size smaller than 0.0001
I don't think your issue is Texture Size value, but not enough geometry of your object. Try to use SubSurf modifier before Displacement modifier.



BTW for such a small details I would use noise texture as Bump Map or for Microdisplacement.

Note: Quite strange for me is that textures for Displacement are different than for shaders - there is not this texture. On other hand, Noise texture node use opposite scale values, like 10000 for similar 0.0001 of Distortion Noise. And with node there in not problem set 1.000.000 :)